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That makes sense! It's easier for me to understand than with functional programming (because I know that very well, while I am just familiar with the basics of OOP), but I see what you mean about JS vs PHP.

I see it more or less working out either way, but with classical inheritance you'd need to pre-define a lot, which may not be the best way to go (the possibility for every entity to be sleeping seems excessive, for example), while with prototypical inheritance you can add those on the go rather than pre-defining them.

(There's also something about "prototypes" in semantics, in that a bird probably can fly, although it doesn't necessarily need to be able to fly-- penguins are birds, but not prototypical birds. That's more about the meaning of words, although it could be extended to relationships as well. If that approach were taken, I can see the prototypical inheritance system being very useful.)

Part of what I think is important is to include structure within the meanings. That is, rather than a "flat" meaning as output, it should be some sort of construct that has separable parts that can be considered independently. As an example, we can think of a meaning like "I see a computer" as a flat meaning-- just a whole meaning that lines up with those words. Or we can think of it as something within internal structure where that whole meaning is still there but we can also refer to parts like "a computer".

DRT is one of the things I'm considering in this approach. Also File-Change Semantics by Heim.

That reminds me of Montague Grammar.

That's the standard theory I'm referring to. It doesn't do well with sub-parts, given that the "meaning" is the meaning of the whole. It isn't incompatible with considering sub-parts, but I've certainly not experienced it as a focus.

As I see it, DRT and its elaborations (Asher, for instance) and / or parallels (Heim) can do at least part of what you seem to need. IN DRT, we can not only grasp the meaning of John is sleeping as a whole, but also specify things about John afterwards, since we first introduce John as a variable x in the representation, and only after that we specify John(x) & Sleep(x) (or x=John & Sleep(x), if you like, but I always considered proper names as predicates in the theory; and of course we should do something about PROG).
In other words, since x has been put in the 'box' (with the help of a DRT-construction rule), we never 'loose' it.
The only weak point of DRT (and of any serious linguistic theory I know) has to do with world knowledge. In the example you gave (I see a computer. It is nice), it refers to the computer (not to the whole sentence). And that's not (exclusively) because of a linguistic rule we could construct but (primarily) because of our knowledge of the world. This knowledge tells us that there are nice computers, ugly computers, fancy computers etc., and also that seeing a computer is not nice per se.
To deal with sentences like the one above, I would like to think of construing a branching DRT-theory which allows for a whole number of possible interpretations after a sentences is processed 'linguistically', after which a world knowledge component should remove the 'pragmatically' impossible ones. (But how can we create a world-knowledge-component? Ask Google?).

I'm not necessarily suggesting that a successful theory has not yet been created. I'm either going to find it, or create it. (Or try!)
[Edit: the fact that I'm not aware of it suggests that at the very least it's seen as peripheral, which to me seems backwards... perhaps in finding it I can help to contribute to promoting it, if it does indeed exist. I found those papers, by the way.]

One thing I have not seen, however, is the concept of "objects", which is what I'm most interesting in here. I really think that someone like Chomsky is significantly influenced by programming and logic before OOP was around and influential-- I think things might have been different if linguistics were re-invented in today's world with OOP around.

I'll check into those references you mentioned certainly.

As for the pragmatics issue, that's certainly true. But I see it as a problem for another day. After all, "It is nice [that I see the computer]" is fine too. It's not as probable/frequent/normal/expected, but there's nothing wrong with it per se. So the grammar will need to generate all possible interpretations-- it=computer; it=[I see a computer]; it=else. Then some other process can work out which one is actually selected.